A goodness-of-fit test for bivariate extreme-value copulas

By Christian Genest, Ivan Kojadinovic, Johanna G. Nevslehov'a, Jun Yan. 2011

96 citations recorded by the source corpus.

Resume: It is often reasonable to assume that the dependence structure of a bivariate continuous distribution belongs to the class of extreme-value copulas. The latter are characterized by their Pickands dependence function. The talk is concerned with a procedure for testing whether this function belongs to a given parametric family. The test is based on a Cramer-von Mises statistic measuring the distance between an estimate of the parametric Pickands dependence function and either one of two nonparametric estimators thereof studied by Genest and Segers (2009). As the limiting distribution of the test statistic depends on unknown parameters, it must be estimated via a parametric bootstrap procedure, whose validity is established. Monte Carlo simulations are used to assess the power of the test, and an extension to dependence structures that are left-tail decreasing in both variables is considered.

Subfields: Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/6b6167d21fe2ee4dd42eaa370cbc2c7f02d20d8a

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Citations in the corpus

Large‐sample tests of extreme‐value dependence for multivariate copulas (2011, background): “Dans le cas bivarié, les auteurs comparent les meilleures versions du test avec le test de Ghoudi et al.(1998) récemment amélioré par Ben Ghorbal et al.”
Multivariate Frequency-Severity Regression Models in Insurance (2016, background): “To determine whether a joint distribution corresponds to an Archimedean copula or a specific extreme-value copula, goodness-of-fit tests developed by [41–44] can be helpful.”
Bivariate flood frequency analysis using the copula function: a case study of the Litija station on the Sava River (2015, methodology): “To distinguish between extreme-value copulas, the Cramér-von Mises II statistical test was applied, which was defined by Genest et al. (2011) SIIn ¼ ∫ 1 0 n An wð Þ Aθn wð Þj j2dw (7) where An(w) is the non-parametric estimator and Aθn is the parametric estimator of the Pickands dependence function…”
Nonparametric estimation of multivariate extreme-value copulas (2011, background): “As in Kojadinovic and Yan (2010) and Genest et al. (2011), the estimators could also be used as a starting point for goodness-of-fit tests, but for brevity we do not pursue this here.”
Copula based analysis of rainfall severity and duration: a case study (2013, methodology): “In addition, for the extreme–value family of copulas, we also use Cramér–von Mises statistic, Sn introduced in Genest et al. (2011) to perform goodness of fit.”